Dynamic Portfolio Selection by Augmenting the Asset Space

We present a novel approach to dynamic portfolio selection that is no more difficult to implement than the static Markowitz model. The idea is to expand the asset space to include simple (mechanically) managed portfolios and compute the optimal static portfolio in this extended asset space. The intuition is that a static choice among managed portfolios is equivalent to a dynamic strategy. We consider managed portfolios of two types: "conditional" and "timing" portfolios. Conditional portfolios are constructed along the lines of Hansen and Richard (1987). For each variable that affects the distribution of returns and for each basis asset, we include a portfolio that invests in the basis asset an amount proportional to the level of the conditioning variable. Timing portfolios invest in each basis asset for a single period and therefore mimic strategies that buy and sell the asset through time. We apply our method to a problem of dynamic asset allocation across stocks, bonds, and cash using the predictive ability of four conditioning variables.

Parameter uncertainty in multiperiod portfolio optimization with transaction costs

We study the impact of parameter uncertainty in multiperiod portfolio selection with trading costs. We analytically characterize the expected loss of a multiperiod investor, and we find that it is equal to the product of two terms. The first term corresponds with the single-period utility loss in the absence of transaction costs, as characterized by Kan and Zhou (2007), whereas the second term captures the multiperiod effects on the overall utility loss. To mitigate the impact of parameter uncertainty, we propose two multiperiod shrinkage portfolios. The first multiperiod shrinkage portfolio combines the Markowitz portfolio with a target portfolio. This method diversifies the effects of parameter uncertainty and reduces the risk of taking inefficient positions. The second multiperiod portfolio shrinks the investor's trading rate. This novel technique smooths the investor trading activity and it also may help to considerably reduce the impact of parameter uncertainty. Finally, we test the out-of-sample performance of our considered portfolio strategies with simulated and empirical datasets, and we find that ignoring transaction costs, parameter uncertainty, or both, results into large losses in the investor's performanceThis work is supported by the Spanish Government through the project MTM2010- 1651

Parameter uncertainty in multiperiod portfolio optimization with transaction costs

We study the impact of parameter uncertainty in the expected utility of a multiperiod investor subject to quadratic transaction costs. We characterize the utility loss associated with ignoring parameter uncertainty, and show that it is equal to the product between the single-period utility loss and another term that captures the effects of the multiperiod mean-variance utility and transaction cost losses. To mitigate the impact of parameter uncertainty, we propose two multiperiod shrinkage portfolios and demonstrate with simulated and empirical datasets that they substantially outperform portfolios that ignore parameter uncertainty, transaction costs, or both

Aligning capital with risk

The interaction of capital and risk is of primary interest in the corporate governance of banks as it links operational profitability and strategic risk management. Senior executives understand that their organization's monitoring system strongly affects the behaviour of managers and employees. Typical instruments used by senior executives to focus on strategy are balanced scorecards with objectives for performance and risk management, including an according payroll process. A top-down capital-at-risk concept gives the executive board the desired control of the operative behaviour of all risk takers. It guarantees uniform compensations for business risks taken in any division or business area. The standard theory of cost-of-capital assumes standardized assets. Return distributions are equally normalized to a one-year risk horizon. It must be noted that risk measurement and management for any individual risk factor has a bottom-up design. The typical risk horizon for trading positions is 10 days, 1 month for treasury positions, 1 year for operational risks and even longer for credit risks. My contribution to the discussion is as follows: in the classical theory, one determines capital requirements and risk measurement using a top-down approach, without specifying market and regulation standards. In my thesis I show how to close the gap between bottom-up risk modelling and top-down capital alignment. I dedicate a separate paper to each risk factor and its application in risk capital management

A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability

We present a simulation-based method for solving discrete-time portfolio choice problems involving non-standard preferences, a large number of assets with arbitrary return distribution, and, most importantly, a large number of state variables with potentially path-dependent or non-stationary dynamics. The method is flexible enough to accommodate intermediate consumption, portfolio constraints, parameter and model uncertainty, and learning. We first establish the properties of the method for the portfolio choice between a stock index and cash when the stock returns are either iid or predictable by the dividend yield. We then explore the problem of an investor who takes into account the predictability of returns but is uncertain about the parameters of the data generating process. The investor chooses the portfolio anticipating that future data realizations will contain useful information to learn about the true parameter values.

Modelling Realized Covariances

This paper proposes a new dynamic model of realized covariance (RCOV) matrices based on recent work in time-varying Wishart distributions. The specifications can be linked to returns for a joint multivariate model of returns and covariance dynamics that is both easy to estimate and forecast. Realized covariance matrices are constructed for 5 stocks using high-frequency intraday prices based on positive semi-definite realized kernel estimates. We extend the model to capture the strong persistence properties in RCOV. Out-of-sample performance based on statistical and economic metrics show the importance of this. We discuss which features of the model are necessary to provide improvements over a traditional multivariate GARCH model that only uses daily returns.eigenvalues, dynamic conditional correlation, predictive likelihoods, MCMC

Bayesian Inference of the Multi-Period Optimal Portfolio for an Exponential Utility

We consider the estimation of the multi-period optimal portfolio obtained by maximizing an exponential utility. Employing Jeffreys' non-informative prior and the conjugate informative prior, we derive stochastic representations for the optimal portfolio weights at each time point of portfolio reallocation. This provides a direct access not only to the posterior distribution of the portfolio weights but also to their point estimates together with uncertainties and their asymptotic distributions. Furthermore, we present the posterior predictive distribution for the investor's wealth at each time point of the investment period in terms of a stochastic representation for the future wealth realization. This in turn makes it possible to use quantile-based risk measures or to calculate the probability of default. We apply the suggested Bayesian approach to assess the uncertainty in the multi-period optimal portfolio by considering assets from the FTSE 100 in the weeks after the British referendum to leave the European Union. The behaviour of the novel portfolio estimation method in a precarious market situation is illustrated by calculating the predictive wealth, the risk associated with the holding portfolio, and the default probability in each period.Comment: 38 pages, 5 figure

Parameter uncertainty in portfolio optimization

La modelización de decisiones reales supone la interacción de dos elementos: un problema de optimización y un procedimiento para estimar los parámetros que definen dicho modelo. Cualquier técnica de estimación requiere de la utilización de información muestral disponible, la cual es aleatoriamente dada. Dependiendo de dicha muestra, los estimadores pueden variar ampliamente, y en consecuencia uno puede obtener soluciones muy distintas del modelo. Concretamente, la incertidumbre de los estimadores que definen el modelo resulta en decisiones inciertas. El análisis del impacto de la incertidumbre de los parámetros en la optimización de carteras es un área muy activo en estadística e investigación operativa. En esta tesis tratamos el impacto de la incertidumbre de los parámetros en la optimización de carteras. En concreto, estudiamos y caracterizamos la pérdida esperada de los inversores que usan información muestral para construir sus carteras optimas, y además proponemos nuevas técnicas para aliviar dicha incertidumbre. Primero estudiamos diferentes criterios de calibración para estimadores shrinkage en el contexto de la optimización de carteras. En concreto consideramos diferentes métodos de calibración para estimadores shrinkage del vector de medias, la matriz de covarianzas y el vector de pesos. Para cada método de calibración damos expresiones explícitas de la intensidad optima del shrinkage y además proponemos un nuevo enfoque no-paramétrico para el cálculo de la intensidad de shrinkage de cada criterio de calibración. Finalmente evaluamos el comportamiento de cada método de calibración con datos simulados y empíricos. En segundo lugar analizamos el impacto de la incertidumbre de los parámetros para un inversor multiperíodo que se enfrenta a costes de transacción. Caracterizamos la pérdida esperada del inversor multiperíodo y encontramos que dicha pérdida es igual al producto de la perdida de un solo periodo y otro término que recoge los efectos multiperíodo en la perdida de utilidad. Además proponemos dos carteras multiperíodo de tipo shrinkage que ayudan a mitigar la incertidumbre de los parámetros. Finalmente analizamos el comportamiento de las carteras multiperíodo que proponemos y encontramos que el inversor puede sufrir grandes pérdidas si ignora los costes de transacción, la incertidumbre de los parámetros o ambos elementos.Modeling every real-world decision involves two elements: an optimization problem and a procedure to estimate the parameters of the model. Any estimation technique requires the utilization of available sample information, which is random. Depending on the given sample, the estimates may vary widely, and in turn, one may obtain very different solutions from the model. Precisely, the uncertainty of the estimates that define the parameters of the model results into uncertain decisions. Analyzing the impact of parameter uncertainty in optimization models is an active area of study in statistics and operations research. In this dissertation, we address the impact of parameter uncertainty within the context of portfolio optimization. In particular, we study and characterize the expected loss for investors that use sample estimators to construct their optimal portfolios, and we propose several techniques to mitigate the impact of parameter uncertainty. First, we study different calibration criteria for shrinkage estimators in the context of portfolio optimization. Precisely, we study shrinkage estimators for both the inputs and the output of the portfolio model. In particular, we consider a set of dffierent calibration criteria to construct shrinkage estimators for the vector of means, the covariance matrix, and the vector of portfolio weights. We provide analytical expressions for the optimal shrinkage intensity of each calibration criteria, and in addition, we propose a novel non-parametric approach to compute the optimal shrinkage intensity. We characterize the out-of-sample performance of shrinkage estimators for portfolio selection with simulatedand empirical datasets. Second, we study the impact of parameter uncertainty in multiperiod portfolio selection with transaction costs. We characterize the expected loss of a multiperiod investor, and we find that it is equal to the product between the single-period utility loss and a second term that captures the multiperiod effects on the overall utility loss. In addition, we propose two multiperiod shrinkage portfolios to mitigate the impact of parameter uncertainty. We test the out-of-sample performance of these novel multiperiod shrinkage portfolios with simulated and empirical datasets, and we find that ignoring transaction costs, parameter uncertainty, or both, results into large losses in the investor's performance